Accurate position tracking is a crucial task in many applications ranging from car navigation over robot control to sports analysis. In order to improve the accuracy of position tracking, we introduce a novel method for constraining Kalman filters by incorporating prior knowledge in an augmented motion model. In contrast to previously reported methods, our approach does not require cumbersome tuning of additional filter parameters and causes less computational overhead. We demonstrate our method in the context of sports analysis in athletics. Using 34 data sets recorded during 400m and 800m runs, we compare our approach to unconstrained and pseudo-measurement filters. The presented augmented motion model in conjunction with an Extended Kalman Filter (EKF) reduced the root mean square error of the filtered output by 60% compared to unconstrained filtering and by 50% compared to a pseudo-measurement EKF.